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We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown strength, the epidemic tend to restart after lifting the restrictions. As a consequence, specific mitigation strategies must be introduced. We characterize the relative importance of different broad strategies by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian regions as separate administrative entities, in which social interactions between age classs occur. Due to the sparsity of the inter-regional mobility matrix, once started the epidemics tend to develop independently across areas, justifying the adoption of solutions specific to individual regions or to clusters of regions. Second, we show that social contacts between age classes play a fundamental role and that measures which take into account the age structure of the population can provide a significant contribution to mitigate the rebound effects. Our model is general, and while it does not analyze specific mitigation strategies, it highlights the relevance of some key parameters on non-pharmaceutical mitigation mechanisms for the epidemics.

By exploiting a bipartite network representation of the relationships between mutual funds and portfolio holdings, we propose an indicator that we derive from the analysis of the network, labelled the Average Commonality Coefficient (ACC), which measures how frequently the assets in the fund portfolio are present in the portfolios of the other funds of the market. This indicator reflects the investment behavior of funds' managers as a function of the popularity of the assets they held. We show that $ACC$ provides useful information to discriminate between funds investing in niche markets and those investing in more popular assets. More importantly, we find that $ACC$ is able to provide indication on the performance of the funds. In particular, we find that funds investing in less popular assets generally outperform those investing in more popular financial instruments, even when correcting for standard factors. Moreover, funds with a low $ACC$ have been less affected by the 2007-08 global financial crisis, likely because less exposed to fire sales spillovers., Comment: 38 pages, 6 figures

We study the international interbank market through a geometrical and a topological analysis of empirical data. The geometrical analysis of the time series of cross-country liabilities shows that the systematic information of the interbank international market is contained in a space of small dimension, from which a topological characterization could be conveniently carried out. Weighted and complete networks of financial linkages across countries are developed, for which continuous clustering, degree centrality and closeness centrality are computed. The behavior of these topological coefficients reveals an important modification acting in the financial linkages in the period 1997-2011. Here we show that, besides the generalized clustering increase, there is a persistent increment in the degree of connectivity and in the closeness centrality of some countries. These countries seem to correspond to critical locations where tax policies might provide opportunities to shift debts. Such critical locations highlight the role that specific countries play in the network structure and helps to situates the turbulent period that has been characterizing the global financial system since the Summer 2007 as the counterpart of a larger structural change going on for a more than one decade., Comment: 24 pages, 11 figures

The recent financial crisis has stressed the need to understand financial systems as networks of interdependent countries, where cross-border financial linkages play the fundamental role. It has also been emphasized that the relevance of these networks relies on the representation of changes follow-on the occurrence of stress events. Adopting a topological approach we are able to address the role that network structures play in the spread of shocks and conversely, the effectiveness of stress events and its impact on the structure of the networks. Here, from series of interbank liabilities and claims over different time periods, we have developed networks of positions (net claims) between countries. Besides the Minimal Spanning Tree analysis of the time-constrained networks, a coefficient of residuality is defined to capture the structural evolution of the network of cross-border financial linkages. Because some structural changes seem to be related to the role that countries play in the financial context, networks of debtor and creditor countries are also developed. Empirical results allows to relate the network structure that emerges in the last years to the globally turbulent period that has characterized financial systems since the latest nineties. The residuality coefficient highlights an important modification acting in the financial linkages across countries in the period 1997-2011, and situates the recent financial crises as replica of a larger structural change going on since 1997., Comment: 22 pages, 8 figures